Fraction Calculator
Add, subtract, multiply or divide fractions and mixed numbers with every step shown — common denominator, cross-cancelling, simplifying — and get the answer as a fraction, mixed number, decimal and percent. Also simplifies and compares fractions.
How it works
a/b + c/d = (a × (L ÷ b) + c × (L ÷ d)) ÷ L, where L = LCD(b, d) · a/b × c/d = (a × c) ÷ (b × d) · a/b ÷ c/d = a/b × d/c · mixed number w n/m = (w × m + n)/m · simplify by dividing top and bottom by their GCF
Adding or subtracting needs a common denominator. The calculator uses the least common denominator (LCD), the smallest number both denominators divide into, so the numbers stay as small as possible. It rewrites each fraction over the LCD and then combines the numerators. Multiplying is straight across — tops together, bottoms together — and when a numerator shares a factor with the other fraction’s denominator, the steps show how to cancel it first. Dividing keeps the first fraction, changes ÷ to × and flips the second. The answer is reduced by the greatest common factor of its top and bottom. It is then shown as a mixed number, a decimal (with the repeating part marked when it never ends) and a percent. Switch on “Use mixed numbers” to type values like 2 3/4 directly. Choose Simplify to reduce a single fraction, with the Euclidean algorithm for its greatest common factor. Choose Compare to see which of two fractions is larger by cross-multiplying.
Worked example
1/2 + 2/3: the least common denominator of 2 and 3 is 6, so 1/2 = 3/6 and 2/3 = 4/6. Adding the numerators gives 7/6, which is already in lowest terms. As a mixed number that is 1 1/6, and as a decimal 1.1(6), with the 6 repeating. With mixed numbers, 2 1/2 × 3 1/4 becomes 5/2 × 13/4 = 65/8 = 8 1/8. To divide, 3/4 ÷ 5/6 becomes 3/4 × 6/5. Cancelling the shared factor 2 between the 6 and the 4 leaves 3/2 × 3/5 = 9/10.
Frequently asked questions
Why do fractions need a common denominator to add?
You can only count pieces that are the same size. Halves and thirds are different sizes, but both convert to sixths (3/6 and 4/6), and sixths add directly. Using the least common denominator keeps the numbers small, so there is less to simplify at the end.
How do I enter a mixed number like 2¾?
Switch on “Use mixed numbers” and type 2 in the whole-number box, 3 as the numerator and 4 as the denominator. The steps show the conversion to the improper fraction 11/4. For a negative mixed number, put the minus sign on the whole number: −2 3/4 means −11/4.
Why does dividing flip the second fraction?
Dividing by a number is the same as multiplying by its reciprocal. Dividing by 2/3 asks how many two-thirds fit, which is the same as multiplying by 3/2. This is often remembered as “keep, change, flip”.
What is cross-cancelling?
Before multiplying, divide a numerator and the other fraction’s denominator by a factor they share. In 4/9 × 3/8, the 4 and 8 share 4 and the 3 and 9 share 3, leaving 1/3 × 1/2 = 1/6. You get the same answer as multiplying first and simplifying 12/72, but with smaller numbers.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. For 42/126 the GCF is 42, so the fraction reduces to 1/3. Choose Simplify to see the GCF found step by step with the Euclidean algorithm.
How can I tell which of two fractions is bigger?
Cross-multiply: compare the first numerator times the second denominator with the second numerator times the first denominator. For 3/4 and 5/7, 3 × 7 = 21 and 5 × 4 = 20, so 3/4 is larger. Choose Compare to do this with your numbers.
Why does the decimal have brackets?
Some fractions never end as decimals. 1/3 is 0.333… and 7/6 is 1.1666… The digits in brackets repeat forever, so 1.1(6) means 1.1666… with the 6 continuing without end. Fractions whose denominator has only 2s and 5s as prime factors, like 3/8, end and have no brackets.
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This calculator is for educational purposes. Double-check important results before acting on them.